Atomic force microscopy cantilever, system and method

ABSTRACT

The surface of the atomic force microscopy (AFM) cantilever is defined by a main cantilever body and an island. The island is partly separated from the main body by a separating space between facing edges of the main body and the island. At least one bridge connects the island to the main body, along a line around which the island is able to rotate through torsion of the at least one bridge. The island has a probe tip located on the island at a position offset from said line and a reflection area. In an AFM a light source directs light to the reflection area and a light spot position detector detects a displacement of a hght spot formed from light reflected by the reflection area, for measuring an effect of forces exerted on the probe tip.

FIELD OF THE INVENTION

The invention relates to a cantilever for use in an atomic forcemicroscopy system, to an atomic force microscopy system and an atomicforce microscopy method.

BACKGROUND

Atomic Force Microscopy (AFM) can be used to form images of samplesurfaces. Moreover, it is known to map structures buried below thesurface using AFM. In an article titled “Detection of buried referencestructures by use of atomic force acoustic microscopy” by A. Striegleret al. published in Ultramicroscopy 111 (2011) 1405-1416 the possibilityof the imaging buried structures has been shown. Such measurements makeuse of the effect that vibration of the surface of buried structureswithin the sample will result in sample surface vibration. Vibrations ofburied structures can be excited e.g. due to excitation of vibrations ofthe sample surface, which may reach the buried structure as ultrasoundwaves.

AFM is an improvement of Atomic Tunnel Microscopy (ATM). In ATM movementof the tip perpendicular to the sample surface is controlled in afeedback loop to maintain a constant electric current through the tipwhile the relative position of the sample and probe tip is scanned in adirection parallel to the surface of the sample to sense the forces as afunction of position on the sample. AFM more generally measures theeffect of forces exerted on the probe tip in interaction with atoms ofthe sample. AFM makes use of a probe tip on a cantilever to sense forcesbetween the probe tip and atoms on the surface of a sample. Inparticular, properties of (near) resonant cantilever vibration may bemeasured to sense forces.

The forces between the probe tip and the sample can be sensed from theireffect on the vibration resonance frequency and/or quality, the phaseand/or amplitude relation between the cantilever vibrationphase/amplitude and ultrasound phase/amplitude. Different kinds of forceinteraction between the probe tip and the sample are possible.

As is known per se any mechanical object like a cantilever has aplurality of resonance modes, wherein each resonance mode corresponds toa resonance frequency and a spatial mode pattern of vibration amplitudeand phase relations. The cantilever is able to vibrate freely with asinusoidal time dependence at the resonance frequency and a spatialpattern with vibration amplitudes in proportion to the amplitudes of themode pattern and phase relations between vibrations at differentpositions according to the phase relations of the mode pattern. Theamplitude and phase of any vibration of the cantilever can berepresented as a sum of such mode patterns, each with its own appliedamplitude factor and phase. In periodically driven vibrations, theamplitude factors become large for the modes of which the resonancefrequency are the same or nearly the same as the excitation frequency.Thus, with excitation frequencies near the resonance frequency of amode, the cantilever vibration substantially corresponds to the modepattern. Spatial positions in the mode pattern where the amplitude iszero are called “nodes” and spatial positions of local maxima of theamplitude of the mode patterns are called “bellies”.

In “tapping” resonance the probe tip is located at a belly of theresonance mode, so that the tip and the sample exchange intense “tap”force peaks in brief, periodic time intervals without significantinteraction outside these time intervals. In contact resonance, theprobe tip is located near a node of the resonance mode, so that the tipand the sample exchange relevant forces continuously, not only in brieftime intervals and the tip and the sample substantially stay in the samespatial relation. Tapping resonance is useful to measure topographicmeasurements and contact resonance is more useful to detect sub-surfacestructure. For both, the cantilever vibration may be measured usingreflection of (laser) light from the cantilever, in which case AFM isalso called laser force microscopy.

U.S. Pat. No. 5,646,339 discusses an adaptation of the cantilever tomake it possible to measure the force exerted on the probe substantiallyindependently in three directions. In order to do so a cantilever isused that has a plurality of excitation modes, which differ from eachother in that they have at different resonance frequencies and involvemovement in different directions. Thus forces in different directionscan be measured by measuring response to excitation of vibrations withdifferent frequencies. In one example, a combination of a transversalvibration mode and a torsional vibration mode is used. The vibrationsare sensed by heterodyne mixing of laser reflection from a forcemeasurement point positioned away from the probe tip, that moves in allthe modes.

SUMMARY

Among others it is an object to provide for an improved Atomic ForceMicroscopy (AFM) system and method, which is particularly suitable formapping buried structures.

An AFM cantilever according to claim 1 is provided. The probe tip of thecantilever is located on an island of the cantilever that is connectedto a main body of the cantilever by at least one bridge along a linearound which the island is able to rotate through torsion of the atleast one bridge. In this way, the probe tip is located so thatdifferent types of cantilever vibration modes, involving vibration ofthe main body and torsion of the island can be excited substantiallyindependently by the interaction between the probe tip and the samplesurface. The bridge will transmit vibrations of the main body to theisland, so that they affect the orientation of the reflection surface.At the same time rotation of the reflection surface also results inorientation changes of the reflection surface, enabling measurement ofboth. Such measurements may be performed one at a time orsimultaneously, using e.g. the frequency and/or directions of theorientation changes to separate the effects of rotation of the islandand vibration of the main body. An AFM system is provided that comprisessuch a light source positioned to direct light to the reflection areaand a light spot position detector positioned to detect a displacementof a light spot formed from light reflected by the reflection area, forusing said displacement to measure an effect of forces exerted on theprobe tip by a surface of a sample.

In an embodiment, the AFM system uses a first one of these modes is usedat near the resonance frequency in a contact resonance mode andsimultaneously a second one of these modes at a low frequency in afeedback loop to control the distance between the cantilever and thesample surface during a scan of the probe tip along the sample surface.

In a embodiment of the cantilever, the island is preferably massbalanced with respect to the line around which the island is able torotate. That is, the center of mass of the island lies in a planeperpendicular to the top surface of the cantilever that runs throughthis line and the parts of islands on opposite sides of this plane haveequal mass. This reduces coupling between rotation of the island andvibration of the main body. However, an island is with some massimbalance of e.g. up to 40% and 60% or up to 25% and 60% of the mass ofthe island on opposite sides may also be used.

The island may be located within an outline of the main body, as viewedfrom above the top surface of the cantilever that is parallel to thesample surface. In an embodiment of the cantilever, the at least onebridge comprise only a first and second bridge, the first bridge and thesecond bridge connecting the island to the main body on opposite sidesof the island, this island lying within an outline of the main body.This makes it easier to excite rotation of is island around the line onwhich the bridges are located and reduces coupling between the rotationand vibration of the main body.

In an embodiment, the main body is mass balanced with respect to theline around which the island is able to rotate. That is, the center ofmass of the main body lies in a plane perpendicular to the top surfaceof the cantilever that runs through this line. In this way, couplingbetween vibration modes of the main body and rotation modes of theislands is minimized.

In an embodiment of the cantilever, the line around which the island isable to rotate extends along a direction of longest size of thecantilever, from the fixed end of the cantilever to its opposite end,e.g., when the surface of the cantilever has a rectangular outline,parallel to the longest edge of the cantilever. As another example, thisline may extend perpendicular to the longest direction. When the lineextends along the direction of longest size of the cantilever, therotation of the island and vibrations of the main body result inreflection displacements in different directions, making it possible toseparate their effect on this basis.

In an embodiment of the cantilever, the main body of the cantilever hasan uneven mass distribution m(x) as function of position x between theends of the cantilever, an average of a product m(x)*u²(x) of the massm(x) and a squared mode shape u²(x) as a function of position x alongthe cantilever divided by an average of u²(x) being larger for a contactvibration mode of order N, with N greater than one, than for a contactvibration mode of order one. In this way the distance between differentorder resonance modes of the main body can be reduced, which makes itpossible to reduce the frequency bandwidth needed to measure effects offorces on a plurality of resonance modes of the main body. This may alsobe used in cantilevers that do not have an island as claimed in claim 1.

In an embodiment of the cantilever, the main body of the cantilever hasan uneven mass distribution m(x) as function of position x between theends of the cantilever the mass distribution having a maximum at a bellyof a contact vibration mode of order N, with N greater than one. This isan effective way of reducing the distance between different orderresonance modes of the main body. This may also be used in cantileversthat do not have an island as claimed in claim 1.

In an embodiment of the cantilever the main body comprises a mainportion, a neck portion and a head portion, the neck portion lyingbetween the main portion and the head portion, the neck portion having asmaller width than the main portion and the head portion, the cantilevercomprising a further reflection area located on the head portion, adifference between a contact resonance frequency of the main body and aresonance frequency of orientation changes of the head portion relativeto the main portion due to bending of the neck portion being less thatthe quality factor of the resonance of said orientation changes of thehead portion times the resonance frequency of the resonance of theorientation changes of the head portion. This may also be used incantilevers that do not have an island as claimed in claim 1: in thatcase the further reflection area may be the only reflection area that isused. When used in combination with the island, reflection from both theisland and the head portion may be measured. The head portion providesfor more sensitive measurements of vibration of the main body than themain body itself. Vibration of the head portion will be driven by themain body, and it provides larger orientation vibration amplitude thanthe orientation vibration amplitude of the main body. The size of theneck portion and/or the mass of the head portion may be adjusted to tunethe resonance frequency of the orientation changes of the head portionrelative to the main portion.

In an embodiment of the AFM system the AFM system comprises a sampleplatform; a vibration generator coupled to the platform and/or thecantilever for generating vibration in the sample and/or the cantilever,a first end of the cantilever being fixed in said vibration; an actuatorfor moving the cantilever and the platform relative to each other, atleast in a height direction perpendicular to the surface of the sampleand a scan direction parallel to the surface of the sample; and acontrol circuit. The control circuit may be configured, e.g. by means ofa control program of a programmable in the control circuit, to controlthe actuator to move the cantilever and the platform relative to eachother progressively in the scan direction; activate the vibrationgenerator to generate vibrations of the sample relative to thecantilever at a frequency of a contact resonance mode of the cantilever;measure properties of vibration of the cantilever in the contactresonance mode from a first component of the displacement duringmovement of the cantilever and the platform relative to each other inthe scan direction, control the actuator to move the cantilever and theplatform relative to each other in the height direction in a feedbackloop in response to a second component of the displacement duringmovement in the scan direction. Thus contact resonance can be measuredcontinuously during the scan or at least most of the time during thescan.

In a further embodiment of the AFM system the light spot positiondetector is configured to distinguish light spot displacements in firstand second, different two dimensional directions, the control circuitbeing configured to derive the first second component of thedisplacement from the light spot displacements in the first and secondtwo dimensional directions. In this way the measurements of torsion ofthe island and vibration of the main body that are transmitted to theisland can be at least partially separated based on the direction of thedisplacement.

In an embodiment of the AFM system the feedback loop comprises a lowpass frequency filter to filter the second component of the displacementfrom an output of light spot position detector. This provides foralternative or further of torsion of the island and vibration of themain body that are transmitted to the island.

In use the cantilever may be used by

-   -   generating vibration of a sample relative to the cantilever at a        frequency of a contact resonance mode of the cantilever;    -   moving the cantilever and the platform relative to each other,        at least in a height direction perpendicular to the surface of        the sample and a scan direction parallel to the surface of the        sample;    -   directing light at the reflection area and measuring        displacement of a light spot due to light reflected by the        reflection area;    -   measuring properties of vibration of the cantilever in the        contact resonance mode from a first component of the        displacement during movement of the cantilever and the platform        relative to each other in the scan direction    -   controlling movement of the cantilever and the platform relative        to each other in the height direction in a feedback loop in        response to a second component of the displacement during        movement in the scan direction.

BRIEF DESCRIPTION OF THE DRAWING

These and other objects and advantageous effects will become apparent ofexemplary embodiments with reference to the following figures.

FIG. 1 shows an AFM system

FIG. 2, 2 a-c show an AFM cantilevers for contact resonance modemeasurement

FIG. 3 shows a control circuit

FIG. 4, 4 a show an AFM cantilevers for contact resonance modemeasurement

FIG. 4b shows mode patterns

FIG. 5 shows an AFM cantilevers for contact resonance mode measurement

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

FIG. 1 shows an AFM system (components not to scale) comprising acantilever 10, a light source 12, a light position detector 14, anactuator 16, an ultrasound transducer 17 and a control circuit 18.Cantilever has a fixed end connected to a cantilever support 102. Aprobe tip 100 is located on cantilever 10 at a distance from the fixedend. A sample 19, which does not form part of the AFM system per se, isshown to illustrate the operation of the AFM system. In the illustratedembodiment, sample 19 is located between ultrasound transducer 17 andcantilever 10, on a sample platform 190 of the AFM system. A surface ofsample 19 faces cantilever 10. Probe tip 100 is directed from cantilever10 towards the surface of sample 19.

Actuator 16 is configured to move sample 19 and cantilever 10 relativeto each other in directions transverse and parallel to the surface ofsample 19, so that probe tip 100 may be moved parallel and transverse tothe surface of sample 19 due to the effect of actuator 16. For the sakeof illustration an x and z direction are indicated that are parallel andperpendicular to the surface of sample 19. By way of example, anactuator 16 for translating cantilever 10 in three directions relativeto a base of the AFM system is shown, with sample 19 fixed on the base.But alternatively an actuator may be used that is configured to move asample platform for sample 19 or both the sample platform and cantilever10 relative to the base to realized movement in one or more of thedirections. Actuator 16 may comprise a plurality of bodies ofpiezoelectric material coupled between the base of the AFM system andcantilever 10 and/or the sample platform. Control circuit 18 may beconfigured to apply voltages to these bodies of piezoelectric materialto cause motion. Alternatively, another type of actuator may be used,such as a magnetic field driven actuator or an actuator that is drivenby electric forces without piezo material.

Ultrasound transducer 17 may similarly comprise one or more bodies ofpiezo electric material. Alternatively, other forms of excitation may beused, such as photothermic excitation. In the illustrated exampleultrasound transducer 17 is used to excite vibrations that travel to theprobe tip through the sample, but alternatively a transducer at adifferent location may be used to excite at the same surface as wherethe probe tip is located, for example via the probe tip or elsewhere onthe surface.

Light source 12, which is preferably a laser light source, is directedto transmit a light beam to a reflection area on cantilever 10 and lightposition detector 14 is placed to receive the light beam afterreflection from the reflection area. The entire upper surface ofcantilever 10 may be reflective, or a part of the upper surface that isequal to or larger than the reflection area may be reflective. Thereflection area is a part of this surface that receives light from lightsource 12. A coating layer or area of e.g. aluminum or gold may beprovided at the upper surface of cantilever 10 to provide for improvedreflection. The reflected light forms a light spot on light positiondetector 14. Light position detector 14 may comprise four photodiodes,located in respective quadrants. Alternatively another light spotposition detector may be used, such as an image sensor, or a pair ofadjacent photodiodes. Control circuit 18 has an input coupled to anoutput of light position detector 14 and outputs coupled to controlinputs of actuator 16. FIG. 2 shows an exemplary cantilever geometrythat allows for vibration in different directions by the main body ofthe cantilever and of an island 24 respectively. This embodiment may becalled a cantilever-in-cantilever geometry. In this geometry, cantilever10 has a rectangular outline, with a fixed end 20 and a free end 22 onopposite sides of the rectangular outline. Preferably fixed end 20 and afree end 22 are the shortest edges of the rectangular outline. In FIG.2, x and y directions are indicated along the direction between fixedend 20 and free end 22 and perpendicular to that direction respectively.Fixed end 20 is connected to the base of the AFM system, e.g. via theactuator (not shown). Free end 22 is permanently connected to the baseonly through cantilever 10 and fixed end 20.

Within the rectangular outline, cantilever 10 comprises an island 24, inthe form of an interior rectangle, that is connected to a main body ofcantilever 10 only at two connecting bridges 26 a,b on two oppositeedges of interior rectangle 24 along a separation between the island andthe main body, midway along these opposite edges. As used herein, anisland is a part of the cantilever that, seen in top view, is connectedto the main body of the cantilever only via one or more connectingbridges that interrupt the separation between the island and the mainbody of the cantilever. In the illustrated embodiment, connectingbridges 26 a,b extend only over part of the opposite edges, e.g. overless than one fifth or one tenth of the opposite edges. The remainder ofthe circumference of interior rectangle 24 is separate from the mainbody of cantilever 10. Connecting bridges 26 a,b may be an integral partof the body of cantilever 10. The cantilever may be formed from a bodyof material and cutting (e.g. laser cutting) or etching through the bodyalong the circumference of interior rectangle 24, except at bridges 26a,b.

As illustrated, connecting bridges 26 a,b are preferably located on thecentral line (in the x-direction) midway the longest edges of therectangular outline of cantilever 10. The longest direction of interiorrectangle 24 may be perpendicular to this central line, i.e. along they-direction. Island 24 may be located near free end 22, or moregenerally not closer to fixed end 20 than to free end 22. A probe tip ata probe tip position 28 and a reflection area 29 are provided on island24 on the surfaces of island 24 that face the sample and face away fromthe sample respectively. As noted the upper surface of the island may beintrinsically reflective or a reflective surface layer may be added. Thereflection area should be large enough to provide for orientationdependent reflection of light from the light source, e.g. with adirection dependent intensity that peaks in a peak direction dependenton the orientation of the reflection surface. The center of the probetip position 28 is offset in the xy plane from the line connectingbridges 26 a,b (offset in the y-direction). In the illustratedembodiment, probe tip position 28 and the position of reflection area 29are offset in the xy plane on opposite sides of the line connectingbridges 26 a,b. Alternatively, reflection area 29 may be located on thisline, or the probe tip position 28 and the position of reflection area29 may be offset in the xy plane on the same side of that line.

The cantilever geometry with an interior rectangle connected by bridgessupports different vibration modes, which substantially correspond tobending of the cantilever as a whole, and rotation of island 24 aroundthe line connecting bridges 26 a,b due to torsion of connecting bridges26 a,b respectively. In the mode that substantially corresponds tobending of the cantilever as a whole there is little or no rotation ofisland 24 and vice versa the same applies to the mode that substantiallycorresponds to rotation of island 24. Therefore, the resonancefrequencies of these modes can be adapted substantially independently,so that both are within measurement range.

Preferably, the mass (volume) of the island 24 is much smaller than thatof the main body of the cantilever (e.g. less than one fourth or onetenth), so that the main body has a substantial mass involved invibration of the cantilever. To ensure that the resonance frequenciesare far apart, bridges 26 a, b that are narrower than the cantilever, sothat the stiffness that acts against independent vibration of island 24is small. Simultaneous movement in more than one mode is provided for,by asymmetry of the position of the position 28 probe tip with respectto the central symmetry line (in the x-direction) of the main body ofthe cantilever. In operation, control circuit 18 controls actuator 16 toscan (preferably translate) the relative position of sample 19 andcantilever 10 in one or two directions (x and/or y direction) parallelto the surface of sample 19. During the scan, light source 12 directs alight beam at reflection area 29 on cantilever 10. Reflection area 29reflects the light beam to light position detector 14, where it forms alight spot at a position that depends on an orientation of reflectionarea 29.

In the illustrated embodiment, the two described modes result inorientation changes of reflection area 29 around two axes, which in turnresult in light spot position changes in two directions at light spotdetector 14. Spot detector 14 detects these position changes. Forexample, when a four quadrant light detector 14 is used, relativechanges of the resulting light intensities detected by four quadrantlight detector 14 are indicative of changes of the position of the lightspot and hence the orientation of reflection area 29. Changes of theorientation of reflection area 29 can be the result of bending of themain body of cantilever 10 (rotation of reflection area 29 around they-direction as a result of bending of cantilever 10 in the x-z plane,)and of rotation of island 24 relative to main body of cantilever 10(rotation of reflection area 29 around the x-axis in a result ofrotation the y-z plane,). Control circuit 18 is configured to derivesignals representing these two rotations, from the light intensitiesthat are detected by four quadrant light detector 14.

In the illustrated embodiment control circuit 18 controls ultrasoundtransducer 17 to excite ultrasound waves at the bottom of sample 19. Theultrasound waves travel through sample 19. At probe tip 100, vibrationsof cantilever 10 are excited due to effects of the ultrasound waves onthe sample. In one embodiment ultrasound transducer 17 is used to exciteultrasound waves at a plurality of frequencies in the sample. Non-linearmixing effects, e.g. between the sample and the probe tip, are used toproduce surface vibrations at a difference frequency. These surfacevibrations result in vibrations of cantilever 10. In turn, thevibrations of cantilever (e.g. bending in the x-z plane) causes periodicrotation of reflecting area 29, which causes periodic deflection oflight from light source 12 and periodic changes of the output signalsfrom light position detector 14. During the scan, ultrasound transducer17 is used to generate vibrations at a frequency or frequencies thatresult in vibrations of cantilever 10 at or near a contact moderesonance frequency of cantilever 10.

As is known per se, contact resonance corresponds to a resonance mode ofcantilever 10 that has a node near the position of probe tip 100. In thecontact mode resonance, the surface orientation of cantilever 10 at thenode varies periodically. The resonance frequencies of such cantilevermodes may be computed analytically or numerically using theEuler-Bernoulli equations of cantilever vibration. Alternatively, one ormore of such frequencies may be determined experimentally.

In a contact resonance mode, probe tip 100 and sample 19 exchangerelevant forces continuously. These forces are affected by elastic andinelastic responses of the sample, including responses due sub-surfacestructures near the surface. These responses in turn affect resonanceproperties, such as the resonance frequency and/or quality. This makescontact mode resonance suitable for detecting and analyzing suchsub-surface structures. Control circuit 18 derives measurements ofproperties of the contact resonance from these periodic changes. This isknown per se. For example, control circuit 18 may determine theamplitude and/or phase of the periodic changes, and/or the resonancefrequency and/or quality. The latter two may be determined for exampleby sweeping the excitation frequency and measuring amplitude and/orphase of periodic changes during the sweep. Control circuit 18 isconfigured to determine the resonance properties using a first componentof light spot position changes, which corresponds to movements that arepart of the contact resonance. For example, when the mode thatsubstantially corresponds to bending of the cantilever as a whole isexcited at or near the contact resonance frequency, rotation ofreflecting area 29 around the y-axis may be measured for this purpose,by measuring in light spot movement in the x direction (the longestdirection of cantilever 10).

Control circuit 18 is configured to control the height of cantileverabove the surface of sample 19 in a feedback loop during the scan, tokeep the rotation of reflecting area 29 around the other axis on averageconstant during the scan. Changes of this rotation are due scanningmotion rather than contact resonance excitation. In the example whereinthe mode that substantially corresponds to bending of the cantilever asa whole is excited at or near the contact resonance frequency, therotation of island 24 around the x-axis relative to main body ofcantilever 10 may be kept on average constant during the scan. For thispurpose, control circuit 18 is preferably also configured to apply lowpass filtering to the signal that represents the rotation component ofreflecting area 29 that is perpendicular to rotation due to the contactresonance, and to use the low pass filtered signal to control the inputsignal of actuator 16 that controls the height of cantilever 10. The lowpass filter bandwidth is selected to ensure suppression of frequencycomponents at frequencies corresponding to contact mode resonancefrequencies.

Preferably, control circuit 18 is configured to measure the rotation inresponse to contact resonance mode excitation simultaneously withcontrolling the height of cantilever above the surface of sample 19 inthe feedback loop, or alternately using measurements of rotationresponse and for control so that the control of the height remainseffective during measurement of the rotation in response to thisexcitation. In theory, the feedback control can be interrupted brieflyduring time intervals that are so short that the height cannot varysignificantly in these intervals, but preferably it is continuous duringthe contact mode resonance measurements.

Although a specific cantilever geometry with an island in the form of aninterior rectangle connected by bridges has been shown, it should beappreciated that other geometries could be used. For example, the islandmay have another shape in the interior of the cantilever, such as anellipse, or a polygon such as a regular hexagon or a bow-tie and/or oneof connecting bridges 26 a,b may be omitted.

FIG. 2a-c show other examples of other layouts. In FIG. 2a,b theposition 28 probe tip and the position of the reflection area 29 are ona first part of the cantilever that is connected to the remainder of thecantilever via a single bridge 26 a, and this first part is exterior tothe remaining part, rather than surrounded by the remaining part. InFIG. 2c , an internal island is shown that rotates around a line in they direction, by torsion of bridges 26 a,b that extend in the y directionon opposite sides of the symmetry line of the main body 20. Instead ofrectangles other shapes may be used for the first part or the bridge. Itshould be noted that FIGS. 2, 2 a-c do not show limitative examples.Other layouts may be used.

Preferably, the probe tip is located offset from an axis of rotation ofthe island around the bridge or bridges. This facilitates excitation ofrotation of this axis by the probe tip. More preferably, the surfaceshape of the island is mirror symmetric about a symmetry line on whichthe bridge or bridges are located, or at least that the mass of theisland is balanced with respect to the axis of rotation, i.e. that thecenter of mass of the island lies substantially on the axis of rotation.This reduces coupling between the rotation of the island and vibrationof the main body of the cantilever. Preferably, the mass of main body isbalanced with respect to the axis of rotation of the island, e.g. thebridge or bridges may lie on a line about which the main body of thecantilever is mirror symmetric. This reduces coupling between therotation of the island and vibration of the main body of the cantilever.

The reflection area is preferably located on the island, so that theorientation of the reflection area will vary both with vibration of theisland and vibration of the main body of the cantilever. The reflectionarea may be located over the rotation axis of the island. When thesurface of the main body of the cantilever is mirror symmetric and thebridge or bridges are located on the mirror symmetry line of the surfaceof the main body, the orientation changes due to rotational vibrationsof the island and vibration of the main body modes are substantiallyperpendicular, so that both can be measured substantially independentlyof each other, from perpendicular motion components of light spotmovement.

However, although substantially perpendicular motions make measurementseasier, they are not indispensable. Low pass filtering may be used tosuppress the effect of contact resonance movement on the feed back loopand/or the direction of the light spot movement component used for thefeedback may be set along a direction along which the contact resonancemovement has no effect. In other embodiments a plurality of reflectionsareas may be used to measure different displacement components. A firstreflections area may be located on the island and a second reflectionsarea may be located elsewhere. Displacements of separate light spots maybe measured.

The cantilever geometries of FIGS. 2, 2 a, 2 b and similar geometriesmake it possible to optimize individual parts of the geometry largelyindependently for feed back and contact resonance. Preferably the partof the geometry whose motion is used for the feed back is made lessstiff than the part used for the contact resonance. For example, whenthe rectangle in rectangle geometry is used, the optical effect ofrotation of the island around the axis through bridges 26 a,b may beused for the feed back. In this case, narrow bridges 26 a,b could beused to reduce stiffness of this rotation and the remainder of thecantilever can be made to have a higher stiffness for use in contactresonance measurements to measure sub-surface structures. Similaroptimizations may be used in similar embodiments such as the embodimentsof FIGS. 2a, b . The cantilever geometries of FIGS. 2, 2 a, 2 b andsimilar geometries also make it possible to maximize the separationbetween the motion direction due to feedback and resonance.

FIG. 3 shows an exemplary embodiment of control circuit 18, comprising ascan signal generator 30, a filter 32, a differential amplifier 33, anoscillator 34 and a detector 36. Scan signal generator 30 may comprisean oscillator with an x and/or y control output coupled to an output oroutputs 30 a of control circuit for connection to x and/or y movementcontrol inputs of the actuator.

An input of filter 32 is coupled to an input 32 a of control circuit forconnection to a first output of the light spot position detector, for asignal indicating spot displacement in a first direction by the lightspot position detector. Differential amplifier 33 has first and secondinputs coupled to an output of filter 32 and a reference input.Differential amplifier 33 has a z control output coupled to outputs 33 aof control circuit for connection to a z movement control input of theactuator.

Oscillator 34 is configured to oscillate at a frequency at or near aresonance frequency of a contact vibration mode of the cantilever.Oscillator 34 has an output coupled to an output 34 a of control circuitfor connection to the ultrasound transducer. An input of detector 36 iscoupled to an input 32 a of control circuit for connection to a secondoutput of the light spot position detector, for a signal indicating spotdisplacement in a second direction by the light spot position detector.Detector 36 may be a synchronous detector, with an input for a referencesignal or signals from oscillator 34 at the frequency at or near aresonance frequency of a contact vibration mode of the cantilever. Inother embodiments, oscillator 34 may be replaced by a pair ofoscillators configured to oscillate at frequencies spaced by thatfrequency.

Although FIG. 3 shows the embodiment in terms of components that may berealized as distinct circuits, control circuit 18 may comprise aprogrammable computer and a memory wherein a computer program is storedto configure the computer to implement part or all of the differentcomponents of the embodiment of FIG. 3 digitally. In addition to theillustrated components, the computer program may provide forpre-processing of the signals from the light spot position detector andpost-processing to the detected vibration properties and for storingmeasurements in correspondence with different scan positions of thegenerated x and/or y scan. Alternatively, or in addition control circuit18 may comprise hardware components to implement part of all of thecomponents.

Contact mode resonance for detecting and/or analyzing effects ofsub-surface structures usually provide only for measurements in alimited stiffness variation range, because the resonance frequency hasan S-shape dependence on stiffness. To provide for more ranges, or alarger range, with a single cantilever it is desirable to be able tomeasure contact resonance changes of a plurality of contact resonancemodes. However, it is undesirable to do so in a way that increasesstiffness too much, as this increases the risk of damage to thesubstrate surface. FIG. 4 illustrates a cantilever 40 design forincreasing the number of contact resonance modes that can be used forthe measurements.

FIG. 4 shows a side view of another embodiment of a cantilever 40 with aprobe tip 400. Herein the thickness of cantilever 40 varies unevenly asa function op position from the fixed end 42 to the location of probetip 400 (along the x-direction). The variation of thickness is shown asan embodiment of an uneven distribution of mass of cantilever 40 as afunction op position from the fixed end 42 to the location of probe tip400. Other embodiments of uneven mass distribution include variation ofthe width of cantilever 40 (in the y direction, cf. FIG. 4a ) and acombination of variation of width and thickness. A maximum 44, ormaxima, of the mass distribution is or are located at the position of abelly or bellies of a contact resonance mode of order N>1 that has nodeat probe tip 400 and a further node between probe tip 400 and fixed end42. As shown, in FIG. 4, a single rise in the height of the top surfacein a belly may be used. Alternatively rises at a plurality of belliesmay be used, and/or lowered bottom surface. Similarly, the width ofcantilever 40 may be increased in multiple bellies on both sides ofcantilever 40 as shown in FIG. 4a , or in a single belly and/or or oneside. Embodiments like FIG. 4, 4 a and their variations may be used incombination with embodiments like those of FIGS. 2, 2 a, 2 b, or ontheir own.

FIG. 4b illustrates mode patterns of orders N=1 and N=2 as a function ofx-positions with on the cantilever: the z displacement at differentx-positions is the product u(x)*f(t) of a mode amplitude u(x) the modepattern with a periodic time dependent function f(t). The x-scale is inFIG. 4b is the same as in FIG. 4. As is known per se, nodes 48 of avibration mode are positions along cantilever 40 at which the z-positiondoes not change as a result of vibration according to the vibrationmode, i.e. where u(x)=0 and bellies 46 are positions where the amplitude|u(x)| of the z-position change is maximal. The number N of bellies 46will be referred to as the order N of the vibration mode.

The resonance frequency of the modes generally increases with increasingorder N. In practice, vibration in vibration modes with resonancefrequencies above that of a critical order Nc are not detectable in anAFM. Often Nc=1 for contact resonances, so that only the lowest ordervibration contact resonance is detectable. A typical maximum detectableresonance frequency in AFM is 5 MHz.

Per se, addition of mass to a cantilever has the effect that it reducesthe resonance frequencies of its vibration modes. This makes it possibleto raise the critical order, e.g. to Nc=2. However, the addition of massalso increases the stiffness of cantilever 40, which increases the riskof damage to the substrate or cantilever 40, and counteracts the effecton the resonance frequency. The uneven mass distribution as a functionof x position with a maximum at a belly 46 of the contact vibration modeof order N=2 makes it possible to improve the ratio between thereduction of the resonance frequency and the increase of the stiffnessfor the mode of order N=2. Thus, for example, the uneven distributionmakes it possible to accomplish the same reduction in resonancefrequency for the contact resonance more of order N=2 with less increasein stiffness and hence less risk of damage. In this way contactresonance modes of more others can be made detectable, e.g. up to N=2,or even up to N=3 or N=4. With more resonance modes effects deeper belowthe sample surface become detectable.

It should be appreciated that this ratio of the effect on frequency andstiffness is maximal when the maximum or maxima of the mass distributionare concentrated at the belly or bellies. But such an optimum is notnecessary to obtain at least some effect. An effective unevennesssuffices. Similarly, for a given mass spread, it is optimal but notnecessary locate the maximum or maxima of the mass distribution at theposition of the belly or bellies.

The effective unevenness can be quantified in terms of a correlationcoefficient C between the square of the mode amplitude factor for acantilever with evenly distributed mass and the actual uneven mass. Sucha correlation coefficient corresponds to <m(x)*u²(x)>/<u²(x), i.e. theaverage, taken over positions x along the length of the cantilever ofthe product m(x)*u²(x) of the mass m(x) and the squared mode shapefactor u²(x) as a function of position x along the cantilever, dividedby the average of u²(x). The average kinetic energy of mode motion isproportional to this correlation coefficient. When the unevennessincreases the ratio C(N_(h))/C(N_(l)) of the correlation coefficients ofmodes N_(h) and N_(l) (e.g. N_(h)=2 and N_(l)=1) the ratiof(N_(h))/f(N_(l)) of their resonance frequencies decreases. Preferably,a mass distribution is used that at least increase the ratioC(N_(h)=2)/C(N_(l)=1) for the second and first mode. This can berealized by increasing the mass around the bellies of the higher ordermode Nh, e.g. by using a mass distribution that has a maximum at thebelly of the higher order mode N_(h), preferably for N_(h)=2 Theembodiment with the uneven mass increase of FIG. 4 may be combined withthe embodiment of FIG. 2 and its use to regulate the height during thescan while contact mode resonance properties are measured.Alternatively, the embodiment with the uneven mass increase may be usedseparately from the embodiment of FIG. 2. The advantage of using acombination of the embodiments of FIGS. 2 and 4 is that more modes canbe measured in parallel with use of the feedback loop.

FIG. 5 shows a top view (in the xy plane) of another embodiment of acantilever 50 wherein the probe tip and the reflecting surface lie indifferent parts of the cantilever that have different motion properties.Cantilever 50 has a main portion 52, a neck portion 54 and head portion56. In this embodiment neck portion 54 lies between head portion 56 andmain portion 52. A plurality of neck portion 54 may be used in parallelbetween head portion 56 and main portion 52. A cantilever 50 with a mainportion 52 and a neck portion 54 would have two underlying types ofvibration: vibration of main portion 52 and vibration of head portion56, if the resonance frequencies of these vibrations would not be closeto each other.

The position of probe tip 500 lies in main portion 52, between neckportion 54 and the fixed end 51 of cantilever 50. In neck portion 54 thewidth of cantilever 50 is smaller than in head portion 56 and mainportion 52 that contains fixed end 53 and probe tip 500. A reflectionarea 58 is provided on head portion 56.

The purpose of the smaller width in neck portion 54 is to make theorientation changes of reflection area 58 as a result of vibration ofmain portion 52 in contact resonance modes larger than the orientationchanges elsewhere on cantilever 50. This improves detectability ofvibration. Instead of the bridge-connected island formed by head portion56 other geometries may be used such as an island connected by more thanone bridge, an island within the main portion of the cantilever and/oran island along the side of the cantilever.

The orientation changes of the head portion due to bending of neckportion 54 are mechanically similar to vibration of the mass of headportion 56 under influence of a spring force provided by neck portion54, with a resonance frequency that is proportional to the square rootof the stiffness of neck portion 54 divided by the mass of head portion56. The width, thickness and/or the length of neck portion 54 may beadjusted to change the stiffness of neck portion 54 in order to tune theresonance frequency. Similarly, the mass of head portion 56 may bechanged to tune the resonance, keeping the mass much smaller than thatof main portion 52 (e.g. less than 10% of the mass of main portion 52).

Preferably a difference between a contact resonance frequency of mainportion 52 and a resonance frequency of orientation changes of headportion 56 relative to main portion 52 due to bending of neck portion 54is less that the quality factor of the resonance of said orientationchanges of head portion 56 times the resonance frequency of theresonance of the orientation changes of head portion 56 and preferablyless than half that product. As is known per se the quality factorcharacterizes a resonator's bandwidth relative to its center frequency.The resonance frequencies can be adjusted to be close to one another byadjusting the mass and/or stiffness of head portion 56 and/or neckportion 54 relative to those of main portion 52. Adding mass andreducing stiffness reduces the resonance frequency and vice versa.Suitable values may be determined experimentally or by simulation.

As a result head portion 56 provides for more sensitive measurements ofvibration of main portion 52 than main portion 52 itself. Vibration ofhead portion 56 will be driven by the main portion 52, and it provideslarger orientation vibration amplitude of head portion 56 than theorientation vibration amplitude of main portion 52.

In contrast to the embodiments of FIG. 2, 2 a, 2 b, the head portion 56and main portion 52 and neck portion 54 are configured so that resonancefrequencies of resonance of the two underlying types of vibration areselected to lie so close to one another that this result in a modepattern that strongly couples the vibration mode patterns of underlyingtypes of vibration of the head portion and the main portion that wouldoccur in the case of disparate resonances frequencies of the headportion and the main portion.

The embodiment with the neck portion of FIG. 5 may be combined with theembodiment of FIGS. 2 and/or 3 and their use to regulate the heightand/or reduce the resonance frequency of the higher order mode(s). In anembodiment the cantilever may have a first and second reflectingsurface, lying on a first and second island part of the cantileverrespectively, that are each connected to the remainder of cantilever byone or more bridges. The probe tip may lie on the first island, whichmay be configured as in FIG. 2 for example, and the second island may beconfigured as shown in FIG. 5. In another or further embodiment, afurther island with the reflections surface may be connected to theisland with the probe tip. In an embodiment the cantilever may have anuneven mass distribution as in the embodiment of FIG. 4 and an islandwith a reflecting surface like head portion 56. Alternatively, theembodiment with the neck portion of FIG. 5 may be used separately fromthe embodiment of FIGS. 2 and/or 4. The advantage of using a combinationof the embodiments of FIGS. 5 and 2 or 4 is that larger amplitudechanges in light spot position are made possible in combination with atleast one of the modes.

1. A cantilever for use in an atomic force microscopy (AFM) system, thecantilever comprising: a main body, the main body forming a part of asurface of the cantilever; an island, the island forming a further partof the surface of the cantilever, the island being partly separated fromthe main body by a separating space between facing edges of the mainbody and the island; at least one bridge connecting the island to themain body along a line around which the island is able to rotate throughtorsion of the at least one bridge; a reflection area located on theisland; and a probe tip located on the island at a position offset fromthe line.
 2. The cantilever according to claim 1, wherein the at leastone bridge consists of a first bridge and a second bridge, the firstbridge and the second bridge connecting the island to the main body onopposite sides of the island, wherein the island lies within an outlineof the main body.
 3. The cantilever according to claim 1, wherein themain body is mass balanced with respect to the line.
 4. The cantileveraccording to claim 1, wherein the line extends along a direction of alongest size of the cantilever.
 5. The cantilever according to claim 1,wherein the main body of the cantilever has an uneven mass distributionm(x) as function of position x between ends of the cantilever, anaverage of a product m(x)*u²(x) of the mass m(x) and a squared modeshape u²(x) as a function of position x along the cantilever divided byan average of u²(x) being larger for a contact vibration mode of orderN, with N greater than one, than for a contact vibration mode of orderone.
 6. The cantilever according to claim 1, wherein the main body ofthe cantilever has an uneven mass distribution m(x) as function ofposition x between ends of the cantilever the mass distribution having amaximum at a belly of a contact vibration mode of order N, with Ngreater than one.
 7. The cantilever according to claim 1, wherein themain body comprises: a main portion, a neck portion and a head portion,wherein the neck portion lies between the main portion and the headportion, wherein the neck portion has a smaller width than the mainportion and the head portion, wherein the cantilever comprises a furtherreflection area located on the head portion, wherein a differencebetween a contact resonance frequency of the main body and a resonancefrequency of orientation changes of the head portion relative to themain portion due to bending of the neck portion being less than thequality factor of the resonance of said orientation changes of the headportion times the resonance frequency of the resonance of theorientation changes of the head portion.
 8. An atomic force microscopy(AFM) system comprising: a cantilever comprising: a main body, the mainbody forming a part of a surface of the cantilever; an island, theisland forming a further part of the surface of the cantilever, theisland being partly separated from the main body by a separating spacebetween facing edges of the main body and the island; at least onebridge connecting the island to the main body along a line around whichthe island is able to rotate through torsion of the at least one bridge;a reflection area located on the island; and a probe tip located on theisland at a position offset from the lien around which the island isable to rotate; a light source positioned to direct a light to thereflection area; and a light spot position detector positioned to detecta displacement of a light spot formed from light reflected by thereflection area, for using said displacement to measure an effect offorces exerted on the probe tip by a surface of a sample.
 9. The AFMsystem according to claim 8, further comprising: a sample platform; avibration generator coupled to the platform and/or the cantilever forgenerating vibration in the sample and/or the cantilever, a first end ofthe cantilever being fixed in said vibration; an actuator for moving thecantilever and the platform relative to each other, at least in a heightdirection perpendicular to the surface of the sample and a scandirection parallel to the surface of the sample; a control circuitconfigured to; control the actuator to move the cantilever and theplatform relative to each other progressively in the scan direction;activate the vibration generator to generate vibrations of the samplerelative to the cantilever at a frequency of a contact resonance mode ofthe cantilever, measure properties of vibration of the cantilever in thecontact resonance mode from a first component of the displacement duringmovement of the cantilever and the platform relative to each other inthe scan direction; and control the actuator to move the cantilever andthe platform relative to each other in the height direction in afeedback loop in response to a second component of the displacementduring movement in the scan direction.
 10. The AFM system according toclaim 9, wherein the light spot position detector is configured todistinguish light spot displacements in a first dimensional directionand a second dimensional direction that differs from the firstdimensional direction, wherein the control circuit is configured toderive the first component of the displacement and the second componentof the displacement from the light spot displacements in the firstdimensional direction and the second dimensional direction,respectively.
 11. The AFM system according to claim 9, wherein thefeedback loop comprises a low pass frequency filter to filter the secondcomponent of the displacement from an output of light spot positiondetector.
 12. A cantilever for use in an atomic force microscopy (AFM)system, the cantilever comprising: a main body, having an uneven massdistribution m(x) as function of position x between ends of thecantilever, an average of a product m(x)*u²(x), of the mass m(x) and asquared mode shape u²(x) as a function of position x along thecantilever, divided by an average of u²(x) being larger for a contactvibration mode of order N, with N greater than one, than for a contactvibration mode of order one; a reflection area located on thecantilever; and a probe tip on the cantilever at a node of the contactvibration modes.
 13. The cantilever according to claim 12, wherein themass distribution has a maximum at a belly of the contact vibration modeof order N.
 14. A cantilever comprising a main portion, a neck portionand a head portion and a probe tip on the main portion, the neck portionlying between the main portion and the head portion, the neck portionhaving a smaller width than the main portion and the head portion,wherein the cantilever comprises a reflection area located on the headportion, wherein a difference between a contact resonance frequency ofthe main portion and a resonance frequency of orientation changes of thehead portion relative to the main portion due to bending of the neckportion is less than the quality factor of the resonance of saidorientation changes of the head portion times the resonance frequency ofthe resonance of the orientation changes of the head portion.
 15. Amethod carried out by a cantilever for atomic force microscopy (AFM),wherein the cantilever comprises: a main body, the main body forming apart of a surface of the cantilever; an island, the island forming afurther part of the surface of the cantilever, the island being partlyseparated from the main body by a separating space between facing edgesof the main body and the island; at least one bridge connecting theisland to the main body along a line around which the island is able torotate through torsion of the at least one bridge; a reflection arealocated on the island; and a probe tip located on the island at aposition offset from the line; and wherein the method comprises:generating vibration of a sample relative to the cantilever at afrequency of a contact resonance mode of the cantilever; moving thecantilever and the platform relative to each other, at least in a heightdirection perpendicular to the surface of the sample and a scandirection parallel to the surface of the sample; directing light at thereflection area and measuring displacement of a light spot due to lightreflected by the reflection area; measuring properties of vibration ofthe cantilever in the contact resonance mode from a first component ofthe displacement during movement of the cantilever and the platformrelative to each other in the scan direction; controlling movement ofthe cantilever and the platform relative to each other in the heightdirection in a feedback loop in response to a second component of thedisplacement during movement in the scan direction.